arXiv subjects

Aidar Dulliev

Publications and source records attributed to Aidar Dulliev.

4 recordsLinked to original sources

arXiv2026

Binomial Transform of Sequences Counting $N$-ary Convexities

We consider the enumeration of $N$-ary convex structures on finite sets. Our main result shows that the total number of convexities is expressed as the binomial transform of the sequence of numbers of grounded convexities. We present the exact numbers of all $N$-ary and grounded $N$-ary convexities for $|X|\leqslant 5$. The obtained integer sequences have been cross-referenced with the OEIS. As a result, we identified both known sequences (such as A000798) and new ones not previously listed.

math.GM↗

arXiv2020

Models and Methods for Three External Ballistics Inverse Problems

We consider three problems of selecting optimal gun barrel direction (or those of selecting optimal semiaxis position) when firing an unguided artillery projectile on the assumption that the gun barrel semiaxis can move in a connected nonconvex cone having a non-smooth lateral surface and modelling visibility zone restrictions. In the first problem, the target is in the true horizon plane of the gun, the second and the third problems deal with some region of 3D space. A distinctive feature of the models is that the objective functions are $\varepsilon$-Lipschitz ones. We have constructed a unified numerical method to solve these problems based on an algorithm of projecting a point onto $\varepsilon$-Lipschitz level function set. A computer program has been based on it. A series of numerical experiments on each problem has been carried out. App. 1.

math.OC↗

arXiv2019

Global optimization of multivariable functions satisfying the Vanderbei condition

We propose two algorithms for solving global optimization problems on a hyperrectangle with an objective function satisfying the Vanderbei condition (this function is also called an $\varepsilon$-Lipschitz continuous function). The algorithms belong to the class of non-uniform cover-ings methods. For the algorithms we prove propositions about convergence to an $\varepsilon$-solution in terms of the objective function. We illustrate the performance of the algorithms using several test numerical examples with non-Lipschitz continuous objective functions.

math.OC↗

arXiv2017

Fractoconvex structures

We define a new structure on a space endowed with convexities, and call it a fractoconvex structure (or, a space with fractoconvexity). We introduce two operations on a set of fractoconvexities and in a special case we show that they satisfy the laws for a distributive lattice. We establish a connection between fractoconvex sets and convex sets using the concept of independent convexities, based on the possibility of representing a fractoconvex set as the intersection of its convex hulls. Finally, we consider some examples of fractoconvexities on the 2-sphere and on $\mathbb Z$.

math.GM↗